Related papers: The Entropy Region is not Closed Under Duality
In Hall's reformulation of the uncertainty principle, the entropic uncertainty relation occupies a core position and provides the first nontrivial bound for the information exclusion principle. Based upon recent developments on the…
We give axiomatic foundations for non-finitary infinite matroids with duality, in terms of independent sets, bases, circuits, closure and rank. This completes the solution to a problem of Rado of 1966.
A special feature of the ground state in a topologically ordered phase is the existence of large scale correlations depending only on the topology of the regions. These correlations can be detected by the topological entanglement entropy or…
The aim of this chapter is twofold. First, we introduce the information loss problem; second, we provide a critical assessment by thoroughly inspecting the assumptions underlying its formulations. In particular, we argue that if we work in…
Using a minimal algebraic model for the thermodynamics of binary rod--polymer mixtures, we provide evidence for a quintuple phase equilibrium; an observation that seems to be at odds with the Gibbs phase rule for two-component systems. Our…
A new kind of duality has been proposed by Carr related to the quantum description of black holes, the so-called Compton/Schwarzschild duality \cite{Carr:2015nqa}. In this context, a new form for a Generalized Uncertainty Principle has…
We prove that the set of quantum correlations for a bipartite system of 5 inputs and 2 outputs is not closed. Our proof relies on computing the correlation functions of a graph, which is a concept that we introduce.
The entanglement entropy of an annulus is examined in a three-dimensional system with or without a gap. For a free massive scalar field theory, we numerically calculate the mutual information across an annulus. We also study the holographic…
Entropic uncertainty relations in a finite dimensional Hilbert space are investigated. Making use of the majorization technique we derive explicit lower bounds for the sum of R\'enyi entropies describing probability distributions associated…
Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
We define an abstract regular polytope to be internally self-dual if its self-duality can be realized as one of its symmetries. This property has many interesting implications on the structure of the polytope, which we present here. Then,…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
We study the entanglement entropy of gauged internal degrees of freedom in a two dimensional symmetric product orbifold CFT, whose configurations consist of $N$ strands sewn together into "long" strings, with wavefunctions symmetrized under…
The structure of isentropes (i.e. level sets of constant topological entropy) including the monotonicity of entropy, has been studied for polynomial interval maps since the 1980s. We show that isentropes of multimodal polynomial families…
We propose a new link between entropy and area: an eternal black hole with an ER bridge with cross-section $A$ can carry a macroscopic amount of quantum information, or be in a mixed state, with entropy bounded by $S \leq A/4G_N$. We…
We examine a class of deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical…
The entanglement entropy of the incompressible states of a realistic quantum Hall system in the second Landau level are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is…
Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded…